The Australian benchmark ASX 200, which barely budged on RBA's widely expected decision, closed up 0.1 percent, or 5.486 points, at 5,484, buoyed by the materials subindex, which rose 0.59 percent, and energy subindex, which gained 0.91 percent.

"Going into the announcement ASX futures had only priced in a 2 percent odds of a cut whilst the AUD remained elevated to back up this consensus view," Matt Simpson, senior market analyst at ThinkMarkets, said in a note after the decision. The Australian dollar traded at $0.7661 against the greenback at 2:46 pm HK/SIN.

Japan's Nikkei 225 finished up 0.83 percent, or 136.98 points, at 16,735.65; In Hong Kong, the Hang Seng index was up 0.22 percent as of 3:06 pm HK/SIN.

China Evergrande Group jumped 8.97 percent in Hong Kong, after it unveiled plans to spin off most of its property assets and list them on the Shenzhen stock exchange in search of a better valuation.

Evergrande said on Monday that it would become the controlling shareholder of Shenzhen Real Estate, after the state-backed Shenzhen property developer issued new shares and cash to an Evergrande subsidiary, in exchange from Chinese property assets.

South Korea's benchmark Kospi closed up 0.55 percent, or 11.23 points, at 2,054.86, with make-up giants making gains.

On Friday, China said it would remove the consumption tax on non-luxury cosmetic products and adjust the consumption tax rate on high-end cosmetics and beauty products to 15 percent from 30 percent, with effect on Oct.1.

The announcement boded well for South Korea's two largest cosmetics companies, with Amorepacific, owner of the Innisfree brand, up 1.41 percent, and LG Household & Health Care up 1.88 percent in response.

China's cosmetics tax cut was also a positive for cosmetics manufacturer Cosmax, which plans to open a new factory in China, Cara Song, an analyst at Nomura, said in a Tuesday report. Shares of Cosmax traded up 6.93 percent.

Also in South Korea, Samsung Group's bio-pharmaceutical manufacturing unit BioLogics said its planned initial public offering was expected to raise up to 2.25 trillion won ($2.04 billion), Reuters reported.

"We think that Patel should have every incentive to error on the side of caution and keep rates constant," Alicia Garcia Herrero, Asia Pacific chief economist at Natixis, said in a Tuesday note. "[However] the risk of a too rapid, and substantial, increase in capital flows into India could tilt the balance towards a cut if he tried to be very forward-looking."

A Reuters poll of economists had a median forecast for the repo rate to be kept at 6.5 percent.

The pound slumped near a 31-year low against the dollar on Monday as markets reacted to U.K. Prime Minister Theresa May's announcement that the Brexit process would begin in early 2017. The currency pair was trading at $1.2776 as of 2:52 pm HK/SIN.

"With a clearer time table, she has brought on more certainties and plans for the two-year negotiation process to leave the EU. However, market is carefully assessing the impact of that, especially with regards to the country's currency. The immediate support level for GBP/USD is at around 1.2800 area," Margaret Yang, market analyst at CMC Markets, said in a Tuesday note.

The U.S. dollar index was at 96.014 against a basket of currencies at 2:52 pm HK/SIN time, up from levels around 95.4 last week.

During the Asian session, U.S. crude futures fell 0.84 percent to $48.40 a barrel, after briefly touching $49.02 overnight, while Brent slipped 0.71 percent to $50.53.

"The lack of bearish news, which traditionally includes higher crude oil production and downside risk to global demand, has left market-watchers nothing to lean on except last week's surprise cut in OPEC oil production," said analysts at OCBC Bank in a Tuesday note.

"Events into the weeks ahead may potentially cap oil gains - US oil inventory data tomorrow (market estimates show another week of gain) and higher OPEC production (Libya production rose and will continue to gain into the months ahead according to officials)," the OCBC analysts said.

Mainland Chinese markets are shut for the Golden Week public holidays.